This is making think the function is contradicting

This is making think the function is contradicting.
the question is asking me to find a function f : N → Z which is one-to-one and has range Z.
the problem is the number is integers in Z is bigger than the number of integers in N.

The only way i can think of is optional function, even that i also have no idea on solving it

This is making think the function is contradicting.
the question is asking me to find a function f : N → Z which is one-to-one and has range Z.
the problem is the number is integers in Z is bigger than the number of integers in N.

The only way i can think of is optional function, even that i also have no idea on solving it